The analysis of the dynamic behaviour of neural networks involving the application of feedback
Although you have not given the entire context but if I were to speculate I would suggest the author is simply trying to tell that Neural Networks are quite difficult to analyse mathematically due to their non-linear nature (due to the use of non-linear activation). There are many questions on this Stack about the mathematical basis of NN.

Do scientists know what is happening inside artificial neural networks?

Also forward propagation is difficult enough, and now we that we have included feedback it becomes exponentially tough. You can easily understand the difficulty posed in such analysis if you take the case of Feedback Amplifiers in electronics. In normal sound amplifiers to avoid distortion we use a negative feedback. This roughly has an inverted waveform compared to i/p signal. It adds up with the input signal and smoothens out the distortions (as opposite wavefroms of not entirely same magnitude adds up). 

|W| > 1 should be the case of Positive feedback, which can cause massive variations in output due to small changes due to its self reinforcing property. The wave-forms are of the same shape and they add up, this results in an even more larger waveform in the next cycle and so on. So probably the author is speaking something along these lines.